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QuestionCalculate 2.74×10−1−6.53×10−42.74 \times 10^{-1} - 6.53 \times 10^{-4}.

Studdy Solution

STEP 1

Assumptions1. We are given two numbers in scientific notation .74×10−1.74 \times10^{-1} and 6.53×10−46.53 \times10^{-4}. . We need to subtract the second number from the first.

STEP 2

To subtract these two numbers, we need to ensure that they have the same exponent. Currently, the exponents are -1 and -4, respectively. We can rewrite the first number with an exponent of -4 by moving the decimal point three places to the right.
2.74×10−1=0.274×100=0.000274×10=0.000274×10−42.74 \times10^{-1} =0.274 \times10^{0} =0.000274 \times10^{} =0.000274 \times10^{-4}

STEP 3

Now that both numbers have the same exponent, we can subtract the coefficients (the numbers in front of the 10−10^{-}).
0.000274−0.000653=−0.0003790.000274 -0.000653 = -0.000379

STEP 4

Finally, we write the result in scientific notation. The coefficient should be a number between1 and10, so we move the decimal point three places to the right and adjust the exponent accordingly.
−0.000379×10−4=−3.79×10−7-0.000379 \times10^{-4} = -3.79 \times10^{-7}So, 2.74×10−1−6.53×10−4=−3.79×10−72.74 \times10^{-1}-6.53 \times10^{-4} = -3.79 \times10^{-7}.

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